Hi Gavin,
Having visited Cyprus twice now, once in August (peak raptor time) and once in late October/November i've got a fair idea of where to go.
Firstly though, may I suggest to you the book 'A Birdwatching Guide to Cyprus' by Arthur Stagg and Graham Hearl, two respected birders who have written books about many Meditterranean countries. Also of interest to you will be the Cyprus bird hotline, which gives an idea of what's about, though I no longer have the number, if you search on Google you'll find something no doubt.
I stayed in Larnaca in August, though i visited the area in November, and there's a plethora of bird site to keep you going. These are:
Cape Greco:
This peninsula can be found south of Protoras, and is a hotspot for Eleonora's Falcons. You could also encounter late migrants/coastal species here, and I imagine there is a possibility of Greater Sand Plover.
Achna Dam: In my opinion the best site in Cyprus, it is very hard to find, but is basically located inland and inbetween Larnaca and Limassol, about 1/2 hours drive from Larnaca. Many species can be found here, and in November i had Spur Winged Plover, Collared Prat, White Pelican, Squacco Heron, Glossy Ibis and Great Reed Warbler, and yielded many more species when i visited in summer.
Askopremos Dam: This is near Paphos, so possibly a litte too far across, but in winter Moustached Warbler may be found here, along with Finsch's Wheatear and Bonelli's Eagle. Near here is Avagas Gorge, where Wallcreeper winter.
Kensington Cliffs: This is near to Limassol, and offers the best views on the island of Eleonoras Falcon and Griffon Vulture.
Paphos Headland: Again maybe too far across, but for me this site yeilded Greater Sand Plover, Isabelline Wheatear, Pygmy Cormorant and Short Toed Lark.
Larnaca Sewage Works: Probably the second best site in Cyprus, and in early winter a truly amazing spectacle. There is a purpose built hide near the salt lake at Larnaca near the airport, and this looks out across two purpose built pools. In early winter these hold Audouins Gull, Slender Billed Gull, Spoonbill, Marsh Sand, Temmincks Stint, Greater Flamingo, White Pelican, 100s of Black Necked Grebe and other wildfowl, with litteraly 1000's of shoveler etc. In the surrounding field Calandra and Bimaculated Lark are a possibility.
There is lots to go at on Cyprus, and i've only touched the surface, though i reccommend purchasing the book afore mentioned, as all these sites are covered with maps etc etc, and a checklist.
Have a good holiday and hope this helps!!!
Dan